Let's determine the slopes of both lines.

Step 1: Find the Slope of Line A

The given equation of Line A is in point-slope form:

$y - 3 = \frac{1}{3} (x - 3)$

The slope-intercept form is:

$y = \frac{1}{3}x - 1$

From this equation, the slope of Line A is $\frac{1}{3}$.

Step 2: Find the Slope of Line B

By observing the graph, Line B passes through points (-6,6) and (6,-6). Using the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-6 - 6}{6 - (-6)} = \frac{-12}{12} = -1$

Thus, the slope of Line B is $-1$.

Step 3: Compare the Slopes

Since $\frac{1}{3}$ is greater than $-1$, we conclude:

$\frac{1}{3} > -1$

Thus, the correct answer is:

• The slope of Line A is $\frac{1}{3}$
• The slope of Line B is $-1$
• The slope of Line A is greater than the slope of Line B.

Would you like further details on any step?

Related Questions:

1. How do you convert an equation from point-slope form to slope-intercept form?
2. What are the different forms of linear equations and when to use them?
3. How do you find the slope of a line given two points?
4. What does the sign of a slope indicate about a line's direction?
5. How do parallel and perpendicular slopes relate to each other?

Tip: A positive slope means the line rises from left to right, while a negative slope means it falls from left to right.